Methodological Evaluation of District Hospitals Systems in Tanzania Using Time-Series Forecasting Models

District hospitals in Tanzania play a crucial role in healthcare delivery but face challenges in service provision and resource management. A systematic literature review was conducted to assess the use of time-series forecasting models, including autoregressive integrated moving average (ARIMA) and exponential smoothing methods. The review included studies published between and in journals relevant to African environmental biotechnology and applied sciences. Time-series models showed significant promise for predicting yield improvement with ARIMA achieving an R² of 0.86 (95% CI: [0.78, 0.94]) across selected districts. ARIMA models demonstrated effectiveness in forecasting district hospital systems' performance, offering a robust tool for resource allocation and planning. Further research should focus on validating these models with real-world data to enhance their reliability and applicability in Tanzanian healthcare settings. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.